I don't know what to say. You assert that the graphs of and are not perpendicular but they clearly are! The two lines intersect where which is the same as or . That is, the two lines intersect at . Now, when x= 2, y= 2x- 2 gives y= 4- 2= 2 so (2, 2) is a another point on the graph of y= 2x- 2.. When x= 0, gives y= 1 so (0, 1) is another point on .
That is, , (2, 2) and (0, 1) form a triangle with points on those two lines. The distance from (6/5, 2/5) to (2, 2) is . The distance from (6/5, 2/5) to (0, 1) is . The distance from (2, 2) to (0, 1) is . But now we see that . That is, the Pythagorean theorem holds- this is a right triangle with hypotenuse the line between (2, 2) and (0, 1). That proves that the intersection is a right triangle.
Perhaps your "squares" aren't true squares and you are "stretching" one way more than the other.
Rereading your post- "The scales I'm using are such that ten small squares on my graph paper represent 1 unit on the x-axis and 2 units on the y-axis", that is exactly what you are doing! If one your x axis is stretched more than your y axis, you certainly are not representing angles correctly. Redraw the graph using ten small squares representing 1 unit on both axes or representing 2 units on both axes.